Journal of Function Spaces The latest articles from Hindawi Publishing Corporation © 2014 , Hindawi Publishing Corporation . All rights reserved. A Unified Approach to Some Classes of Nonlinear Integral Equations Wed, 03 Sep 2014 10:37:32 +0000 We are going to discuss some important classes of nonlinear integral equations such as integral equations of Volterra-Chandrasekhar type, quadratic integral equations of fractional orders, nonlinear integral equations of Volterra-Wiener-Hopf type, and nonlinear integral equations of Erdélyi-Kober type. Those integral equations play very significant role in applications to the description of numerous real world events. Our aim is to show that the mentioned integral equations can be treated from the view point of nonlinear Volterra-Stieltjes integral equations. The Riemann-Stieltjes integral appearing in those integral equations is generated by a function of two variables. The choice of a suitable generating function enables us to obtain various kinds of integral equations. Some results concerning nonlinear Volterra-Stieltjes integral equations in several variables will be also discussed. Nurgali K. Ashirbayev, Józef Banaś, and Raina Bekmoldayeva Copyright © 2014 Nurgali K. Ashirbayev et al. All rights reserved. Ulam’s Type Stability and Fixed Points Methods Wed, 03 Sep 2014 09:08:23 +0000 Janusz Brzdęk, Liviu Cădariu, Krzysztof Ciepliński, Ajda Fošner, Zbigniew Leśniak, and Bing Xu Copyright © 2014 Janusz Brzdęk et al. All rights reserved. Locally Lipschitz Composition Operators in Space of the Functions of Bounded -Variation Mon, 01 Sep 2014 07:35:09 +0000 We give a necessary and sufficient condition on a function under which the nonlinear composition operator , associated with the function , , acts in the space and satisfies a local Lipschitz condition. Odalis Mejía, Nelson José Merentes Díaz, and Beata Rzepka Copyright © 2014 Odalis Mejía et al. All rights reserved. A Note on Starshaped Sets in 2-Dimensional Manifolds without Conjugate Points Thu, 28 Aug 2014 11:49:42 +0000 Let be complete, simply connected n-dimensional Riemannian manifolds without conjugate points. Assume that is starshaped where . For every point , define : y lies on some geodesic segment in S from x to a point of kerS. There is a finite collection of all maximal sets whose union is S. Further, ker in . Adem Kılıcman and Wedad Saleh Copyright © 2014 Adem Kılıcman and Wedad Saleh. All rights reserved. Existence and Uniqueness of Periodic Solutions for Second Order Differential Equations Wed, 27 Aug 2014 07:56:29 +0000 We study some second order ordinary differential equations. We establish the existence and uniqueness in some appropriate function space. By using Schauder’s fixed-point theorem, new results on the existence and uniqueness of periodic solutions are obtained. Yuanhong Wei Copyright © 2014 Yuanhong Wei. All rights reserved. Spectral Distribution of Transport Operator Arising in Growing Cell Populations Mon, 25 Aug 2014 10:46:44 +0000 Transport equation with partly smooth boundary conditions arising in growing cell populations is studied in space. It is to prove that the transport operator generates a semigroup and the ninth-order remainder term of the Dyson-Phillips expansion of the semigroup is compact, and the spectrum of transport operator consists of only finite isolated eigenvalues with finite algebraic multiplicities in a trip . The main methods rely on theory of linear operators, comparison operators, and resolvent operators approach. Hongxing Wu, Shenghua Wang, and Dengbin Yuan Copyright © 2014 Hongxing Wu et al. All rights reserved. The Boundedness of Marcinkiewicz Integrals Associated with Schrödinger Operator on Morrey Spaces Wed, 20 Aug 2014 11:10:55 +0000 Let be a Schrödinger operator, where belongs to some reverse Hölder class. The authors establish the boundedness of Marcinkiewicz integrals associated with Schrödinger operators and their commutators on Morrey spaces. Dongxiang Chen and Fangting Jin Copyright © 2014 Dongxiang Chen and Fangting Jin. All rights reserved. Spaces on the Unit Circle Wed, 20 Aug 2014 06:25:02 +0000 We introduce a new space of Lebesgue measurable functions on the unit circle connecting closely with the Sobolev space. We obtain a necessary and sufficient condition on such that , as well as a general criterion on weight functions and , , such that . We also prove that a measurable function belongs to if and only if it is Möbius bounded in the Sobolev space . Finally, we obtain a dyadic characterization of functions in spaces in terms of dyadic arcs on the unit circle. Jizhen Zhou Copyright © 2014 Jizhen Zhou. All rights reserved. -Contractive Mappings on Generalized Quasimetric Spaces Mon, 18 Aug 2014 07:41:53 +0000 We consider the existence of a fixed point of -contractive mappings in the context of generalized quasimetric spaces without Hausdorff assumption. The obtained results extend several results on the topic in the literature. Erdal Karapınar and Hosein Lakzian Copyright © 2014 Erdal Karapınar and Hosein Lakzian. All rights reserved. Anisotropic Two-Microlocal Spaces and Regularity Sun, 17 Aug 2014 12:24:05 +0000 We define --anisotropic two-microlocal spaces by decay conditions on anisotropic wavelet coefficients on any --anisotropic wavelet basis of . We prove that these spaces allow the characterizing of pointwise anisotropic Hölder regularity. We also prove an anisotropic wavelet criterion for anisotropic uniform regularity. We finally prove that both this criterion and anisotropic --two-microlocal spaces are independent of the chosen anisotropic --orthonormal wavelet basis. Mourad Ben Slimane Copyright © 2014 Mourad Ben Slimane. All rights reserved. Stability for the Mixed Type of Quartic and Quadratic Functional Equations Sun, 17 Aug 2014 11:31:53 +0000 We establish the general solutions of the following mixed type of quartic and quadratic functional equation: . Moreover we prove the Hyers-Ulam-Rassias stability of this equation under the approximately quartic and the approximately quadratic conditions. Young-Su Lee, Soomin Kim, and Chaewon Kim Copyright © 2014 Young-Su Lee et al. All rights reserved. The Relationship between Two Involutive Semigroups and Is Defined by a Left Multiplier T Sun, 17 Aug 2014 00:00:00 +0000 Let be a semigroup with a left multiplier T on . There exists a new semigroup , which depends on and T, which has the same underlying space as . We study the question of involutions on and a Banach algebra . We find a condition of T under which and the second dual admit an involution. We will show that is -algebra if and only if is an isometry, under mild conditions. Also, is -algebra if and only if so is , under other minor conditions. S. M. Mohammadi and J. Laali Copyright © 2014 S. M. Mohammadi and J. Laali. All rights reserved. Fixed Point Theory and the Ulam Stability Wed, 13 Aug 2014 09:14:40 +0000 The fixed point method has been applied for the first time, in proving the stability results for functional equations, by Baker (1991); he used a variant of Banach's fixed point theorem to obtain the stability of a functional equation in a single variable. However, most authors follow the approaches involving a theorem of Diaz and Margolis. The main aim of this survey is to present applications of different fixed point theorems to the theory of stability of functional equations, motivated by a problem raised by Ulam in 1940. Janusz Brzdęk, Liviu Cădariu, and Krzysztof Ciepliński Copyright © 2014 Janusz Brzdęk et al. All rights reserved. Riesz Basicity for General Systems of Functions Tue, 12 Aug 2014 09:14:46 +0000 In this paper we find the general conditions for a complete biorthogonal conjugate system to form a Riesz basis. We show that if a complete biorthogonal conjugate system is uniformly bounded and its coefficient space is solid, then the system forms a Riesz basis. We also construct affine Riesz bases as an application to the main result. A. M. Sarsenbi and P. A. Terekhin Copyright © 2014 A. M. Sarsenbi and P. A. Terekhin. All rights reserved. Existence of Positive Solutions for Some Superlinear Fourth-Order Boundary Value Problems Mon, 11 Aug 2014 06:11:18 +0000 We are concerned with the following superlinear fourth-order equation , where are nonnegative constants such that and is a nonnegative continuous function that is required to satisfy some appropriate conditions related to a class satisfying suitable integrability condition. Our purpose is to prove the existence, uniqueness, and global behavior of a classical positive solution to the above problem by using a method based on estimates on the Green function and perturbation arguments. Imed Bachar and Habib Mâagli Copyright © 2014 Imed Bachar and Habib Mâagli. All rights reserved. A Mathematical Analysis of Fractional Fragmentation Dynamics with Growth Thu, 07 Aug 2014 10:40:34 +0000 We make use of the theory of strongly continuous solution operators for fractional models together with the subordination principle for fractional evolution equations (Bazhlekova (2000) and Prüss (1993)) to analyze and show existence results for a fractional fragmentation model with growth characterized by its growth rate . Indeed, strange phenomena like the phenomenon of shattering (McGrady and Ziff (1987)) and the sudden appearance of infinite number of particles in some systems with initial finite particles number could not be fully explained by classical models of fragmentation or aggregation. Then, there is an increasing volition to try new approaches and extend classical models to fractional ones. In the growth model, one of the major challenges in the analysis occurs when is integrable at , the minimum size of a cell. We restrict our analysis to the case of integrability of at . This case needs more considerations on the boundary condition, which, in this paper, is the McKendrick-von Foerster renewal condition. In the process, some properties of Mittag-Leffler relaxation function Berberan-Santos (2005) are exploited to finally prove that there is a positive solution operator to the full model. Emile Franc Doungmo Goufo Copyright © 2014 Emile Franc Doungmo Goufo. All rights reserved. On Extremal Problems in Certain New Bergman Type Spaces in Some Bounded Domains in Tue, 05 Aug 2014 10:59:04 +0000 Based on recent results on boundedness of Bergman projection with positive Bergman kernel in analytic spaces in various types of domains in , we extend our previous sharp results on distances obtained for analytic Bergman type spaces in unit disk to some new Bergman type spaces in Lie ball, bounded symmetric domains of tube type, Siegel domains, and minimal bounded homogeneous domains. Romi F. Shamoyan and Olivera Mihić Copyright © 2014 Romi F. Shamoyan and Olivera Mihić. All rights reserved. Generalized Steffensen Type Inequalities Involving Convex Functions Tue, 05 Aug 2014 00:00:00 +0000 In this paper generalized Steffensen type inequalities related to the class of functions that are “convex at point ” are derived and as a consequence inequalities involving the class of convex functions are obtained. Moreover, linear functionals from the difference of the right- and left-hand side of the obtained generalized inequalities are constructed and new families of exponentially convex functions related to constructed functionals are derived. Josip Pečarić and Ksenija Smoljak Kalamir Copyright © 2014 Josip Pečarić and Ksenija Smoljak Kalamir. All rights reserved. Molecular Characterization of Hardy Spaces Associated with Twisted Convolution Tue, 22 Jul 2014 06:54:01 +0000 We give a molecular characterization of the Hardy space associated with twisted convolution. As an application, we prove the boundedness of the local Riesz transform on the Hardy space. Jizheng Huang and Yu Liu Copyright © 2014 Jizheng Huang and Yu Liu. All rights reserved. Estimates of Intrinsic Square Functions on Generalized Weighted Morrey Spaces Tue, 22 Jul 2014 06:49:15 +0000 We prove the boundedness of the intrinsic functions on generalized weighted Morrey spaces , including the strong type estimates and weak type estimates. Moreover, we define the kth-order commutators generated by functions and intrinsic functions, and obtain their strong type estimates on . In some cases, we improve previous results. Guilian Gao and Xiaomei Wu Copyright © 2014 Guilian Gao and Xiaomei Wu. All rights reserved. Smooth Decompositions of Triebel-Lizorkin and Besov Spaces on Product Spaces of Homogeneous Type Tue, 22 Jul 2014 06:37:06 +0000 We introduce Triebel-Lizorkin and Besov spaces by Calderón’s reproducing formula on product spaces of homogeneous type. We also obtain smooth atomic and molecular decompositions for these spaces. Fanghui Liao, Zongguang Liu, and Xiaojin Zhang Copyright © 2014 Fanghui Liao et al. All rights reserved. On Convergence of Fixed Points in G-Complete Fuzzy Metric Spaces Sun, 20 Jul 2014 12:38:28 +0000 We provide some results on the convergence of the sequence of fixed points for some different sequences of contraction mappings or fuzzy metrics in G-complete fuzzy metric spaces with the H-type t-norms. We improve the corresponding conclusions in the literature. Dong Qiu and Shuai Deng Copyright © 2014 Dong Qiu and Shuai Deng. All rights reserved. A Modified Analytic Function Space Feynman Integral and Its Applications Sun, 20 Jul 2014 06:56:08 +0000 We analyze the generalized analytic function space Feynman integral and then defined a modified generalized analytic function space Feynman integral to explain the physical circumstances. Integration formulas involving the modified generalized analytic function space Feynman integral are established which can be applied to several classes of functionals. Seung Jun Chang, Jae Gil Choi, and Hyun Soo Chung Copyright © 2014 Seung Jun Chang et al. All rights reserved. Remarks on the Unimodular Fourier Multipliers on α-Modulation Spaces Thu, 17 Jul 2014 07:24:24 +0000 We study the boundedness properties of the Fourier multiplier operator on -modulation spaces and Besov spaces . We improve the conditions for the boundedness of Fourier multipliers with compact supports and for the boundedness of on . If is a radial function and satisfies some size condition, we obtain the sufficient and necessary conditions for the boundedness of between and . Guoping Zhao, Jiecheng Chen, and Weichao Guo Copyright © 2014 Guoping Zhao et al. All rights reserved. Multilinear Singular Integral Operators on Generalized Weighted Morrey Spaces Thu, 17 Jul 2014 06:55:12 +0000 The purpose of this paper is to discuss the boundedness properties of multilinear Calderón-Zygmund operator and its commutator on the generalized weighted Morrey spaces. Yue Hu, Zhang Li, and Yueshan Wang Copyright © 2014 Yue Hu et al. All rights reserved. Existence and Asymptotic Stability of Solutions of a Functional Integral Equation via a Consequence of Sadovskii’s Theorem Wed, 16 Jul 2014 00:00:00 +0000 Using the technique of measures of noncompactness and, in particular, a consequence of Sadovskii’s fixed point theorem, we prove a theorem about the existence and asymptotic stability of solutions of a functional integral equation. Moreover, in order to illustrate our results, we include one example and compare our results with those obtained in other papers appearing in the literature. Agnieszka Chlebowicz, Mohamed Abdalla Darwish, and Kishin Sadarangani Copyright © 2014 Agnieszka Chlebowicz et al. All rights reserved. On Monotonic and Nonnegative Solutions of a Nonlinear Volterra-Stieltjes Integral Equation Wed, 09 Jul 2014 08:57:50 +0000 We study the existence of monotonic and nonnegative solutions of a nonlinear quadratic Volterra-Stieltjes integral equation in the space of real functions being continuous on a bounded interval. The main tools used in our considerations are the technique of measures of noncompactness in connection with the theory of functions of bounded variation and the theory of Riemann-Stieltjes integral. The obtained results can be easily applied to the class of fractional integral equations and Volterra-Chandrasekhar integral equations, among others. Tomasz Zając Copyright © 2014 Tomasz Zając. All rights reserved. Asymptotic Study of the 2D-DQGE Solutions Mon, 07 Jul 2014 09:31:27 +0000 We study the regularity of the solutions of the surface quasi-geostrophic equation with subcritical exponent . We prove that if the initial data is small enough in the critical space , then the regularity of the solution is of exponential growth type with respect to time and its norm decays exponentially fast. It becomes then infinitely differentiable with respect to time and has value in all homogeneous Sobolev spaces for . Moreover, we give some general properties of the global solutions. Jamel Benameur and Mongi Blel Copyright © 2014 Jamel Benameur and Mongi Blel. All rights reserved. Hyers-Ulam Stability of Differentiation Operator on Hilbert Spaces of Entire Functions Sun, 06 Jul 2014 09:11:46 +0000 We investigate the Hyers-Ulam stability of differentiation operator on Hilbert spaces of entire functions. We give a necessary and sufficient condition in order that the operator has the Hyers-Ulam stability and also show that the best constant of Hyers-Ulam stability exists. Chun Wang and Tian-Zhou Xu Copyright © 2014 Chun Wang and Tian-Zhou Xu. All rights reserved. Change of Scale Formulas for Wiener Integrals Related to Fourier-Feynman Transform and Convolution Thu, 26 Jun 2014 11:42:39 +0000 Cameron and Storvick discovered change of scale formulas for Wiener integrals of functionals in Banach algebra on classical Wiener space. Yoo and Skoug extended these results for functionals in the Fresnel class and in a generalized Fresnel class on abstract Wiener space. We express Fourier-Feynman transform and convolution product of functionals in as limits of Wiener integrals. Moreover we obtain change of scale formulas for Wiener integrals related to Fourier-Feynman transform and convolution product of these functionals. Bong Jin Kim, Byoung Soo Kim, and Il Yoo Copyright © 2014 Bong Jin Kim et al. All rights reserved.